Sure, let's fill in the missing particle in this nuclear chemical equation step by step.
Given the nuclear reaction:
[tex]$
{}_2^3 He + {}_1^1 H \rightarrow {}_2^4 He + \square
$[/tex]
First, let's understand what the symbols and numbers represent:
- [tex]\({}_2^3 He\)[/tex] is a Helium-3 nucleus with an atomic number (number of protons) of 2 and a mass number (number of protons and neutrons) of 3.
- [tex]\({}_1^1 H\)[/tex] is a Hydrogen-1 nucleus (a proton) with an atomic number of 1 and a mass number of 1.
- [tex]\({}_2^4 He\)[/tex] is a Helium-4 nucleus with an atomic number of 2 and a mass number of 4.
We need to find the atomic and mass numbers of the unknown particle represented by the square.
Let's start with the conservation of atomic numbers. The sum of the atomic numbers on the left-hand side of the equation must equal the sum of the atomic numbers on the right-hand side.
The atomic numbers on the left-hand side are:
[tex]\( Atomic\ number_{left} = 2\ (He-3) + 1\ (H-1) = 3 \)[/tex]
The atomic numbers on the right-hand side are:
[tex]\( Atomic\ number_{right} = 2\ (He-4) + Atomic\ number_{\square}\)[/tex]
Since these must be equal:
[tex]\( 3 = 2 + Atomic\ number_{\square} \)[/tex]
Solving for the atomic number of the unknown particle:
[tex]\( Atomic\ number_{\square} = 3 - 2 = 1 \)[/tex]
Next, let's move on to the conservation of mass numbers. The sum of the mass numbers on the left-hand side of the equation must equal the sum of the mass numbers on the right-hand side.
The mass numbers on the left-hand side are:
[tex]\( Mass\ number_{left} = 3\ (He-3) + 1\ (H-1) = 4 \)[/tex]
The mass numbers on the right-hand side are:
[tex]\( Mass\ number_{right} = 4\ (He-4) + Mass\ number_{\square}\)[/tex]
Since these must be equal:
[tex]\( 4 = 4 + Mass\ number_{\square} \)[/tex]
Solving for the mass number of the unknown particle:
[tex]\( Mass\ number_{\square} = 4 - 4 = 0 \)[/tex]
Thus, the unknown particle has an atomic number of 1 and a mass number of 0. This corresponds to a positron or an electron neutrino in certain contexts. In this case, it is likely a positron or more commonly known as a proton for practical purposes.
Therefore, the complete nuclear equation is:
[tex]$
{}_2^3 He + {}_1^1 H \rightarrow {}_2^4 He + {}_1^0 p
$[/tex]
